So now the big question. Who gets to fish in the English Channel? France? England? Whoever catches them first?

I would guess that intenational law would apply (after the exit period) and that there would be a wiggly line drawn at the half way point between the shorelines of the two countries (unless the continental shelf provision applies, not sure what happens then). That's assuming a no-deal Brexit.

If there is an agreement upon Brexit then there could be a phase in period or a new treaty related to fishing so it would remain to be seen in that case.